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Plurisubharmonic functions in almost complex manifolds. (Fonctions PSH sur une variété presque complexe.) (French. Abridged English version) Zbl 1013.32019
Summary: Let \((M,J)\) be an almost complex manifold. An upper semi-continuous map \(u:(M,J)\to [-\infty,+ \infty[\) is said to be plurisubharmonic if \(u\circ \varphi\) is subharmonic for every pseudo-holomorphic curve: \(\varphi: (\Delta, J_0)\to (M,J)\). By using regularization techniques for currents and Taylor series expansions in suitable coordinates with respect to the structure \(J\), we prove that an upper semi-continuous map \(u:(M,J)\to [-\infty,+ \infty [\) which is not identically equal to \(-\infty\) is plurisubharmonic if and only if the \((1,1)\)-part of \(-dJ^*du\) is (semi-)positive as a current.

MSC:
32U05 Plurisubharmonic functions and generalizations
32Q60 Almost complex manifolds
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[2] Demailly, J.-P., Regularization of closed positive currents of type (1,1) by the flow of a Chern connection, (), 105-126 · Zbl 0824.53064
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